PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
600112^76572-8382636Lelio R Paula11/2015
60023^173191-2^17319182634Mike Oakes02/2004
600314^72072-1582604Lelio R Paula11/2015
6004(55459*2^274339+1)/382589Lelio R Paula06/2014
60052^274351+12382588Lelio R Paula06/2012
6006(1017*2^274339-1)/351582584Lelio R Paula04/2015
60076^106086+11382551Lelio R Paula12/2015
6008(17*10^82540-377)/982541Robert Price11/2017
60092^274093-5869582511Lelio R Paula07/2013
60107*10^82509-4782510Robert Price02/2017
60112^274081-655582507Lelio R Paula07/2013
60132^274074-274074+182505Robert Price10/2014
601414^71985+4782505Lelio R Paula11/2015
60125*10^82504+2182505Robert Price01/2017
60156^106014-13982495Lelio R Paula12/2015
6016(2^274046+47)/75382494Lelio R Paula12/2012
60172^274008-183809982485Enzo Doria05/2015
60182^273981-11002982477Enzo Doria04/2014
601919^64490-3082467Lelio R Paula12/2015
60212^273785+1171582418Lelio R Paula07/2013
60208*10^82417+5182418Robert Price05/2017
602211^79133-1082409Theodore Burton11/2005
602391^42063+9082404Norbert Schneider01/2016
60252^273662-6382381Lelio R Paula06/2012
60242^273661+25582381Lelio R Paula07/2013
6026(62*10^82377-17)/982378Robert Price09/2015
60272^273608+52428782365Paul Underwood08/2018
60288*10^82360-5182361Robert Price10/2017
6029(79*10^82347-1)/382349Robert Price11/2017
6030(11*10^82323+91)/382323Robert Price02/2017
6031(189977#+19081)/(19081*17260483)82317Makoto Morimoto10/2017
6032(189977#+196924)/(2*7*13*541*28874441)82316Makoto Morimoto10/2017
603315^69984+3282308Lelio R Paula11/2015
60349*6^105746+782288Lelio R Paula10/2014
603589^42211-8882286Norbert Schneider01/2016
6036gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
6037(19*10^82270-43)/382271Robert Price10/2017
60382^273282-11024182267Enzo Doria05/2014
6039(13^73849+4^73849)/1782263Robert Price05/2013
604110^82254+9^(82254+1)82255Robert Price08/2016
604010^82254+45777382255Patrick De Geest12/2016
604210^82254-9960982254Patrick De Geest12/2016
6043(754*10^82250-7)/982252Robert Price11/2017
604418^65524+1382251Lelio R Paula11/2015
60452^273206-10782244Lelio R Paula06/2012
60462^273193-45914582240Enzo Doria05/2015
60482^273126+3693782220Yves Minet06/2010
604739505!2+12882220Robert Price03/2015
60492^273053-11211182198Enzo Doria06/2014
60502^273016+118582187Lelio R Paula07/2013
6051(2^273008+3)/782183Lelio R Paula12/2012
60525^117554-1538682167Enzo Doria02/2013
6053(38*10^82161+403)/982162Robert Price11/2017
60542^272907-11143982154Enzo Doria05/2014
6055(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
60562^272875-6982144Lelio R Paula06/2012
60577^97197+482141Robert Price01/2014
6058(4*6^105554+1)/582137Serge Batalov10/2014
60592^272826-443382129Yves Minet03/2019
60606^105531-10982120Lelio R Paula12/2015
60612^272766-6582111Lelio R Paula06/2012
606219^64205-7882103Lelio R Paula12/2015
60632^272702+186997982092Enzo Doria05/2016
6064(29*2^272687-1)/982088Lelio R Paula02/2014
6065(5*10^82085-119)/382086Robert Price04/2016
60662^272660-11004982079Enzo Doria04/2014
60676^105474+6782075Lelio R Paula12/2015
60682^272637+8287582072Lelio R Paula07/2013
60692^272587-3182057Lelio R Paula06/2012
6070(41*10^82044-59)/982045Robert Price10/2017
60718*5^117368+982038Lelio R Paula10/2014
6072(101525^16384+1)/13107482023Lelio R Paula11/2011
60734*5^117343-782020Lelio R Paula10/2014
6074(265*10^81990+17)/381992Robert Price05/2016
60753^171843+1081990Robert Price10/2013
6076(7*10^81985+107)/381986Robert Price02/2017
6077(3*2^272356+1)/17716381983Lelio R Paula12/2012
60782^272296-11114981970Enzo Doria05/2014
6079(9*2^272243-1)/781954Lelio R Paula02/2014
60802^272177-11122381934Enzo Doria05/2014
6081(151009^15817+1)/15101081912Faysal YAtim06/2017
6082(16*10^81896-19)/381897Robert Price03/2016
6083(2^271922+78557)/6381855Lelio R Paula12/2012
6084(10^81848+77)/381848Robert Price01/2017
6085(24737*2^271883+1)/375781846Lelio R Paula06/2014
608610^81778+3981779Robert Price03/2011
608710^81778-17199981778Patrick De Geest07/2013
6088(14*10^81767-11)/381768Erik Branger09/2014
60892^271541+186841781742Enzo Doria04/2016
6090(2^271549-1)/23874968248781734Jens K. Andersen02/2009
60912^271484-16781725Lelio R Paula06/2012
6092(8*10^81709-611)/981709Robert Price11/2017
60932^271382+1290981695Lelio R Paula07/2013
609449^48334+4881694Norbert Schneider07/2014
60957^96668+4881694Lelio R Paula10/2015
609611^78435-141081682Enzo Doria12/2012
60975*10^81653+981654Dmitry Domanov11/2010
6098(2^271211-1)/61396149515981631Jens K. Andersen02/2009
60993^171068+5281621Lelio R Paula12/2015
61002^271115-11040781614Enzo Doria05/2014
61012^271111-11063581613Enzo Doria05/2014
61022^271098-11181609Lelio R Paula06/2012
6103(77*10^81606+13)/981607Robert Price10/2015
61042^271064-279020981599Enzo Doria03/2016
6105(13*2^271053-1)/309581593Lelio R Paula02/2014
61062^271040-5781592Lelio R Paula06/2012
6107(14*10^81585+73)/381586Robert Price04/2016
6108127^38779+12681584Norbert Schneider02/2015
610918^64966-4381551Lelio R Paula11/2015
6110(2^270840+47)/59181529Lelio R Paula12/2012
611120^62654+8781515Lelio R Paula01/2016
6112(19*10^81488+191)/381489Robert Price01/2017
61138*10^81487+2181488Robert Price02/2017
6114(73*10^81485+107)/981486Robert Price08/2016
6115536^29847+29847^53681458Norbert Schneider03/2017
61168*7^96378+981450Lelio R Paula10/2014
61172^270546-11034581443Enzo Doria05/2014
611813^73105-6081435Lelio R Paula11/2015
611944^49524+4381391Norbert Schneider06/2014
6120(3*2^270368-1)/1381389Lelio R Paula02/2014
6121(10^81363+719)/981363Serge Batalov12/2014
6122(10^81353+449)/981353Serge Batalov12/2014
612314^70978-8981350Lelio R Paula11/2015
612411^78108-204081342Enzo Doria12/2012
61253^170400-5881302Lelio R Paula12/2015
6126(17*10^81300-131)/381301Robert Price12/2017
612710^81297+3699181298Patrick De Geest06/2013
612810^81297-5781297Robert Price05/2011
61292^270055-11304781295Enzo Doria07/2014
613018^64759-5581291Lelio R Paula11/2015
6131(2^269987+1)/381274H.&R. Lifchitz10/2000
6132(31^54493-1)/3081268Alexander Zhirkov10/2010
6133(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
61342^269819-459781224Yves Minet03/2019
6135(2^269816+7)/42490181218Lelio R Paula12/2012
6136(23*10^81214+1)/381215Serge Batalov06/2009
6137(17*2^269720+1)/30381193Lelio R Paula07/2012
613856^46441-55^4644181188Robert Price10/2013
61392^269664+17781177Lelio R Paula06/2012
6140(13*2^269665-1)/18581177Lelio R Paula02/2014
61412^269539-11224981140Enzo Doria06/2014
6142((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
6144(2^269495-5)/981126Lelio R Paula12/2012
61431239^26228+26228^123981126Norbert Schneider10/2019
61452^269490-362381125Yves Minet10/2009
6146(55459*2^269444+1)/3581114Lelio R Paula06/2014
6147(2^269417+78557)/525781099Lelio R Paula12/2012
61484*5^116011-781089Lelio R Paula10/2014
61497*10^81058+7981059Robert Price02/2017
61502^269236-10990781049Enzo Doria04/2014
6151(8*10^81029-11)/381030Erik Branger03/2014
61523*10^81021+781022Erik Branger11/2013
61536^104115+10381018Lelio R Paula12/2015
61542^269120+186915181014Enzo Doria05/2016
61555^115901+1281012Lelio R Paula10/2015
6156(2^269083-9)/32036980997Lelio R Paula12/2012
615717^65810-2080976Lelio R Paula11/2015
615820^62236-2380971Lelio R Paula01/2016
61592^268974-11218180970Enzo Doria06/2014
6161L(387433)80969Renaud Lifchitz11/2003
6160V(387433)80969Serge Batalov03/2015
6162(2^268955-509203)/580963Lelio R Paula12/2012
6163(87398^16384+1)/6553780957Lelio R Paula11/2011
6164329^32160+32160^32980954Norbert Schneider11/2014
61652^268859-15980935Lelio R Paula05/2012
6166(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
61682^268827+577580925Lelio R Paula07/2013
61672^268824-11025580925Enzo Doria05/2014
61692^268798-186832180917Enzo Doria04/2016
61702^268753-11462180903Enzo Doria05/2015
61712^268743+160580900Lelio R Paula07/2013
61726^103954-13980892Lelio R Paula12/2015
617310^80883+4980884Robert Price03/2011
617410^80883-8032780883Patrick De Geest07/2013
61756^103937+12180879Lelio R Paula12/2015
6176148^37266+14780877Norbert Schneider12/2018
6177(26*10^80875-119)/380876Robert Price07/2016
6178(22699*2^268657+1)/635180875Lelio R Paula06/2014
61792^268581-86968810580851Lelio R Paula05/2016
6180(11*2^268521-1)/380834Lelio R Paula02/2014
61812^268516-24980832Yves Minet02/2012
61822^268500+1609580827Lelio R Paula07/2013
61833^169402+10080826Lelio R Paula12/2015
61849^84698+8^(84698-1)80823Robert Price03/2016
61852^268472-10973980819Enzo Doria04/2014
6186(9*2^268454+1)/3780813Lelio R Paula12/2012
6187(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
6188134^37987-133^3798780803Jean-Louis Charton12/2005
618915^68702-7680800Lelio R Paula11/2015
61902^268408+780799Lelio R Paula05/2012
61912^268375+14180789Lelio R Paula05/2012
619212^74856-4780784Lelio R Paula11/2015
61932^268346+52428780781Paul Underwood08/2018
61946^103770-10780749Lelio R Paula12/2015
61963^169224-6280741Lelio R Paula12/2015
6195p(16866)#/2+6480741Robert Price03/2017
61975^115502-7280733Lelio R Paula10/2015
61982^268079-192780700Yves Minet10/2009
61992^268028+11780685Lelio R Paula05/2012
6200121^38738+12080683Norbert Schneider01/2015
6201(3^169097-8)/83580677Lelio R Paula12/2012
62022^267918+6780652Lelio R Paula05/2012
6203(89*10^80650-179)/980651Robert Price11/2017
6204(302*10^80638+13)/980640Robert Price01/2017
62053^169004+266080636Lelio R Paula12/2015
62062^267860-11285980634Enzo Doria06/2014
62072^267828-11070580625Enzo Doria05/2014
62082^267743+1270580599Lelio R Paula07/2013
6209(22*10^80595+23)/980596Robert Price03/2015
62102^267674-5180578Lelio R Paula05/2012
6211(86*10^80571-41)/980572Robert Price11/2015
62122^267612-196580560Lelio R Paula07/2013
62132^267553+409780542Lelio R Paula07/2013
62147^95276-880518Robert Price01/2014
6215(15185*2^267457-1)/4782980513Lelio R Paula04/2015
62166^103467+16380513Lelio R Paula12/2015
6217(7*10^80490+143)/380491Robert Price04/2016
621886^41597-85^4159780470Robert Price04/2015
621913^72237+3080468Lelio R Paula11/2015
622017^65389+1480458Lelio R Paula11/2015
6221423^30634+30634^42380456Norbert Schneider05/2017
62222^267232+10580445Lelio R Paula05/2012
622311^77237-307200080435Enzo Doria01/2013
62242^267116-45995980410Enzo Doria06/2015
622538715!2+880406Robert Price01/2015
6226(2^267017+1)/380380H.&R. Lifchitz09/2000
62272^266968-4580366Lelio R Paula05/2012
622820^61768-6380363Lelio R Paula01/2016
62292^266920-11296780351Enzo Doria06/2014
62308*10^80342+8780343Robert Price10/2017
623112^74428-1380322Lelio R Paula11/2015
62322^266680+2780279Lelio R Paula05/2012
62332^266630-13180264Lelio R Paula05/2012
62342^266598+7681980254Enzo Doria05/2016
62352^266587+188063380251Enzo Doria10/2016
62362^266541-11004980237Enzo Doria04/2014
623738635!2-880222Robert Price06/2015
62383^168111+168111^3-180210Robert Price04/2014
62392^266443+51380208Lelio R Paula07/2013
6240(26*10^80200+61)/380201Robert Price06/2017
62412^266412-10991380199Enzo Doria04/2014
6242(10223*2^266417+1)/4509180199Lelio R Paula06/2014
62432^266413-469380199Yves Minet05/2019
624413^71988+6680191Lelio R Paula11/2015
624511^77002-432080190Enzo Doria01/2013
624618^63879-1380186Lelio R Paula11/2015
62472^266368-11229580185Enzo Doria06/2014
6248(3^168050+5)/102145480175Lelio R Paula10/2012
6249(22*10^80167+41)/980168Robert Price02/2015
6250(34*10^80162-43)/980163Ray Chandler12/2010


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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